The 20-year-old scored two goals in 16 matches after joining the Saddlers on a temporary basis back in October.
His loan officially expired on January 5 with Scrimshaw having now returned to the South Coast.
Walsall boss Darrell Clarke said: “We’d like to thank Jake for his efforts during his spell with us and wish him well for the future.
“I’d also like to thank Bournemouth for allowing us to have Jake on a free loan.”
Walsall also confirmed that fellow loanee Adan George has returned to Blues, his parent club.
The forward failed to make a single appearance for the club in his brief time at the Banks's Stadium.
A statement from Walsall said: "Walsall Football Club would like to thank Bournemouth and Birmingham for allowing both players to join on free loans and we wish both players all the best for the future."